A model to evaluate factors controlling growth in Eucalyptus plantations of southeastern Australia

if p f < nf/Cp

and n~' = nf

if pf ~_~nf/Cp

Here Cp is the foliar N / P ratio above which P is considered to be more limiting than N, pf is the foliar P concentration and c is the constant defined in Eq. 3. Fine root allocation a r is also

related to nr* using an equation similar to Eq. 10. (Note that analogous relationships apply to the understorey in these and the following expressions for P dynamics.) Tree P content is simulated using a difference equation similar to Eq. 14 describing N dynamics, except that a larger fraction of P is retranslocated from senescing above-ground tissue (Raison et al., 1993), i.e.,

Pt +1 = Pt + Pup - 0 . 3 5 p f l f F - P b( lb + lw)B - p r l r R -Pwlw W

(41)

The foliar P concentration is then given by

pf = e / ( F + brpR + bbpB + bwpW )

(42)

where brp = 1.8br,, bwp= 1.8bwn a n d bbp= 1.2bbn, i.e., the ratios of a given tree part [P] to foliar [P] are 1.8 X the corresponding ratios for nitrogen (Kirschbaum et al., 1992), except for the case of bark and twigs where the factor 1.2 is required to provide agreement with the P vs. N concentrations in nonfoliar litterfall reported by Raison et al. (1993). Difference equations for P contents of litter and slow and passive pool dynamics are similar to those for N, as given by Eqs. 17-21. P release in organic matter decomposition is given by Pmin = 0"2KLPL + g s e s 'j- g p e p

(43)

and the total P available for plant uptake (in competition with other soil components) by Pavait = (1 --Lp)(Pmi n + Pdep)

(44)

cf. Eqs. 17 and 27. The portion of the above available P taken up by plants, eupmin, is then calculated as a rectangular hyperbolic function of total understorey plus overstorey fine root biomass (Rtot): Pupmin = eavail X R t o t / ( Rto t -k- Mmin)

(45)

where Minin is the half-saturation root biomass at which roots take up half of the mineralized P, the rest being fixed to the soil. Thus, the value of Mmin specifies the relative affinity of soil vs. roots for mineral P. However, trees also have the capacity to take up inorganic P that is fixed to soil particles. This

D.A. King/Ecological Modelling 87 (1996) 181-203

190

fixed P includes loosely h e l d c o m p o n e n t s that can be r e m o v e d by mild c h e m i c a l r e a g e n t s a n d c r o p

m o r e t i g h t l y f i x e d P in i r o n - a n d a l u m i n u m - b o u n d f o r m s w h i c h h a v e b e e n r e p o r t e d as P s o u r c e s f o r

plants adapted

to p h o s p h o r u s - r i c h , glacially de-

Eucalyptus ( M u l l e t t e a n d E l l i o t t , 1974). T h u s , I

r i v e d soils o f t h e n o r t h e r n h e m i s p h e r e , as w e l l as

include two additional pools composed of labile

Table 1 Definition of model parameters and their values for E. sieberi forests in East Gippsland, Victoria, Australia Parameter

Definition

Value

no

critical foliar N concentration above which N no longer limits production for overstorey critical foliar N concentration for understorey exponent defining production efficiency as a power function of foliar N concentration in Eq. 3 foliar N / P ratio above which production is considered to be limited by phosphorus light extinction coefficient for overstorey light extinction coefficient for understorey parameters defining water limitation of production as a function of absorbed light in Eq. 4 age at which overstorey light-use efficiency starts to decline coefficient indicating rate of decline of light-use efficiency with increasing age in Eq. 5 loss coefficients for overstorey foliage, fine roots, bark and twigs, and stemwood and large branches loss coefficients for understorey foliage, fine roots and woody biomass foliar allocation coefficient for overstorey foliar allocation coefficient for understorey specific leaf area of overstorey initial specific leaf area of overstorey seedlings specific leaf area of understorey in full shade age by which overstorey has completely shifted to adult foliage potential maximum biomass production rate for young overstorey canopy, not limited by water or nutrients that absorbs all incident light corresponding potential maximum production rate for understorey atmospheric N deposition atmospheric P deposition fraction of mineralized N lost from the system fraction of mineralized P lost from the system half-saturation root biomass at which roots take up half the mineralized P, the rest fixed to soil theoretical maximum labile P uptake rate per unit labile P by a very dense root system corresponding maximum rate per unit inorganic P half-saturation root biomass for labile P uptake half-saturation root biomass for inorganic P uptake rate at which labile P shifts to inorganic pool rate at which inorganic P shifts to labile pool

0.012 g N g 1 biomass

nuo c Cp k

kuo a, b

ageo Cd lf, lr, lb, l w luf, lur, luw

Ca Cua O" O'initial Cruo

dur Gmax

Gumax Ndep

Pdep LN Lp

Mmin gmax|ab rma×inorg Mlab Minorg glab ginorg

0.016 g N g - 1 biomass 0.4 20 0.5 0.7 0.65, 0.75 20 yrs 0.015 yr- l 0.5, 1, 0.08, 0.01 yr x 0.667, 1, 0.2yr -1 0.23 0.5 4.5 m 2 kg-1 13.5 m 2 kg ~ 14 m 2 kg- x 4 yr 4.4kgm e y r i

3.3kgm 2yr 1 0 . 4 g m 2yr l O.O16gm 2 y r - I 0.01 0.005 0.2 kg m -2 0.3 yr 1 0.03 yr- x 0.2 kg m -2 lkgm 2 0.3 yr -1 0.003 yr- 1

D.A. King/Ecological Modelling 87 (1996) 181-203

and nonlabile inorganic P. Plant uptake from the labile pool is estimated with the following rectangular hyperbolic function: Puptab = Vmaxlab X Piab X R t o t / ( mlab + R t o t )

Pupinorg = VmaxinorgX Pinorg X Rtot/(Minor . + Rtot) (47) where the parameter definitions are completely analogous to those describing labile P uptake. (Because tightly bound P that is solubilized by root exudates may be rapidly taken up by the adjacent roots, I model the transfer of inorganic P to the plant as a single step, rather than as inorganic P ~ labile P ~ plant.) Total plant uptake of P is then (48)

This uptake and its components are then reduced as the foliar N / P ratio declines below Cp, consistent with observations of decreased P uptake in excised roots of fertilized eucalypt saplings (Raison et al., 1993). The labile and inorganic P pool dynamics are expressed as Plabt +1 = Plabt + KinorgPinorg - Klab ]91abt + Pavail -- Pupmin - Puplab

(49)

Pinorgt+ 1 = Pinorgt + KlabPlab -- KinorgPinorgt

- Pup,°o g

Kla b is set equal to a value much greater than

Kinorg, so that Pinorg >> Plab, as is observed (Attiwill and Leeper, 1987).

(46)

where MI~b is the half-saturation fine root biomass for taking up labile P, Plab is the size of the labile P pool and Vm~xl~b is the theoretical maximum labile P uptake rate per unit labile P for a very dense rooting system. P uptake from the more tightly bound nonlabile inorganic P pool is given by

Pup = Pupmin q- Pupl,b + Pu0i.o,g

191

(50)

where KI~b and K~no~g indicate the rates at which P is transferred from the labile to the inorganic pool and vice versa. I assume that all available mineralized P not taken up directly by plants initially enters the labile pool and moves subsequently into the inorganic pool, consistent with the observation that P moves much more quickly into the labile pool but is more tightly bound in the inorganic pool (Attiwill and Leeper, 1987).

2.8. Model application

The model was applied to forests dominated by E. sieberi in East Gippsland, in the region between Orbost and Cann River, Victoria, Australia (37°40'S, 148°45'E). These forests are located on infertile sandy gradational and duplex soils which are particularly deficient in phosphorus. The parameter values shown in Table 1 were derived from characteristics reported for other eucalypt forests and from descriptions of the above East Gippsland forests by Raison et al. (1991,1993). The critical foliar nitrogen concentration, no, indicating an adequate nutrient supply may be taken as the mean foliar N concentration, nf, of canopies on particularly fertile sites (McMurtrie, 1991). Values of nf of 0.017 g N g - l dry mass were reported for very productive E. regnans plantations grown on fertile soils in New Zealand (Frederick et al., 1985). However, E. sieberi typically grows on much less fertile sites than E. regnans Boland et al., 1984) and species adapted to less fertile sites generally have lower nutrient requirements for growth (Pastor and Post, 1986). Thus, n o was set equal to 0.012 for E. sieberi, considerably higher than the observed value of 0.009 in the East Gippsland forests. The critical nitrogen concentration for the understorey vegetation was set at a somewhat higher value (Table 1), as the typical understorey of ferns, grasses and shrubs is thinner leaved than the eucalypt overstorey. Foliar nitrogen concentration per unit biomass generally increases as specific leaf area increases (Reich et al., 1992). The exponent c relating production efficiency to foliar nitrogen concentration was set equal to the rather low value of 0.4, as production may be less sensitive to foliar nitrogen concentration when it is limited by water during part of the year (Thompson and Wheeler, 1992), as is the case for the forests under consideration here. The parameter Cp, the foliar N / P ratio, above which phos-

192

D.A. King~Ecological Modelling 87 (1996) 181-203

phorus limits growth was set equal to 20, twice the value chosen by Sands et al. (1992) in describing the influence of phosphorus vs. nitrogen on the specific leaf area of E. grandis seedlings. However, the latter species commonly occurs on fertile sites. The fact that very productive E. regnans plantations on a fertile site at New Zealand (Frederick et al., 1985) had a foliar N / P ratio of 13, while the stands modelled here had a foliar N / P ratio of 28 and responded strongly to P fertilization (Raison et al., 1993), supports the above choice for cp. The light extinction coefficient depends on leaf orientation, foliage distribution and light angles integrated over the year. Mature E. sieberi foliage, which is held at a near-vertical angle will have a low light extinction coefficient for vertical light and a much higher extinction coefficient for low angles of incident light as occur early and late in the day and during winter. The annual light extinction coefficient used here was set equal to 0.5, as has been used in other eucalypt models (Sands et al., 1992; West, 1993). The understorey light extinction coefficient was set at a somewhat higher value (Table 1), as it has a more horizontal leaf orientation than the overstorey. The parameters defining water limitation of production were set such that the production predicted for a canopy intercepting all light would be 0.75 × that for the non-water-stressed case, approximately equal to the ratio of annual precipitation to pan evaporation for the region of interest (Commonwealth of Australia, 1986). The parameters describing aging effects on production efficiency (age n and c d of Table 1) were chosen to be consistent with the empirical yield model STANDSIM for E. sieberi (John Coleman, CSIRO Division of Forestry, pers. commun.; Campbell et al., 1979). The loss coefficients for different tissues were based on eucalypt leaf lifespans of Keith (1991) and West (1993), the ratio of bark to wood P content given by Attiwill and Leeper (1987) (which is affected by the bark loss rate) and stem volume loss rates reported for temperate species by Harmon et al. (1993). The specific leaf area of understorey leaves, and the parameters describing the specific leaf area of juvenile and adult overstorey leaves were based

on measured patterns in East Gippsland (King, unpublished data). The potential maximum production rate for an overstorey, not limited by nutrients and water that intercepted all light, was then set equal to a value such that the calibrated model would approximate the observed foliage litter production and expected wood production by forests in the area of interest. The potential maximum production rate for the understorey was set to 3 / 4 of the overstorey value, as the understorey receives a greater fraction of its light during times when the sun is high and less blocked by steeply angled eucalypt leaves, which is also a time of greater limitation of photosynthesis by water deficits. The atmospheric N and P deposition rates were set equal to the rather low values of 0.4 and 0.016 g m -2 yr -1, respectively, based on values reported for a few widely scattered sites in Eastern Australia (Feller, 1981; Raison et al., 1985; Attiwill and Leeper, 1987). The fractions of mineralized N and P lost from the system were set equal to 0.01 and 0.005, respectively, as mineralized P may be more tightly bound to the soil than mineralized N. The last 7 parameters of Table 1, specifying phosphorus dynamics, were adjusted to be consistent with reported interactions between phosphorus and soil components (e.g. Attiwill and Leeper, 1987), the tissue P concentrations reported by Raison et al. (1991,1993) and the assumption that soil P pools are approaching equilibrium in oldgrowth forests. Thus, the maximum uptake rate of labile P by roots (Vm~ab) was set equal to 10 × the maximum uptake rate of the more tightly bound, less mobile inorganic P pool and Klab, defining the rate of P movement from the labile to the inorganic P pool was set equal to 100 x ginorg , the parameter defining the reverse flow between these pools. The half-saturation root biomass for uptake of mineralized P was set equal to 0.2 kg m -2, resulting in the prediction that old forests take up about 2 / 3 of the mineralized P directly, with the rest of the mineral P moving first to the labile and then to the inorganic pool, with plant uptake from these latter pools maintaining them at equilibrium. The coefficient Minorg, the half-saturation root biomass

D.A. King/Ecological Modelling 87 (1996) 181-203 Table 2 Initial values of the state variables Variable

Definition

Initial value (g m 2)

F R B W

Overstorey foliage dry mass Overstorey fine root dry mass Overstorey bark dry mass Overstorey woody dry mass Understorey foliage dry mass Understorey fine root dry mass Understorey woody dry mass Slow organic matter nitrogen Passive organic matter nitrogen Fine litter nitrogen Woody litter nitrogen Slow organic phosphorus Passive organic phosphorus Fine litter phosphorus Woody litter phosphorus Labile phosphorus Inorganic phosphorus

0.0036 0.0036 0.00016 0.00064 2 2 2 100 100 31 10 5 5 1.1 0.6 0.8 5

Fu Ru

Wu Us Np NL

NWL Ps

PP PL

PWL Plab Pinorg

The live components are reset to the initial values shown here after every rotation, while the other components continue on their respective trajectories. Pinorg includes that portion of the total inorganic P that could be eventually solubilized and taken up by plants adapted to P-deficient soils, i.e. it does not include occluded P which is completely removed from circulation. The initial value for Plab is substantially higher than during midrotation due to the release of labile P by the initial slash burn.

193

woody litter for a 100-year interval, followed by the nutrient losses and transfers associated with a postharvest slash burn, as described below. Thus, it is assumed that a mature forest had been harvested and the remaining debris burned before the sowing of seed, as is typically done in regenerating eucalypts (Cremer et al., 1978). Multiple rotations were then simulated for several alternative management practices. Based on the transfer of nutrients to the atmosphere in control burns of litter and understorey vegetation reported by Raison et al. (1985), I assumed that postharvest regeneration fires remove 60% of the N content and 40% of the P content of the remaining debris after harvest, with the remaining N entering the litter pool and the remaining P entering the labile P pool. The burnt debris was assumed to include all overstorey bark, twigs and leaves not removed at harvest and the aboveground understorey and fine litter. The simulations also assume that 80% of the total live woody tissue is harvested, approximating the case where all stem and large branch wood is removed, but not stumps and structural and coarse roots.

3. Results and discussion

3.1. General patterns

for inorganic P uptake was set to the higher value of 1 kg m -2 as this component of uptake is dependent on solubilization of P by root exudates (Gardner et al., 1983), and may therefore increase with increasing root density until the entire bulk soil lies within the chemically altered rhizosphere. In the simulations that follow, the initial overstorey foliar biomass was set equal to 0.0036 g m-2, as estimated for newly germinated E. sieberi seedlings at a typical replanting density of 2 seedlings m -2. The initial understorey foliar biomass was set equal to 2 g m -2 based on the existence of stored reserves in those herbaceous understorey plants which resprout from underground rhizomes after disturbance. The initial values for the soil and litter nutrient pools, shown in Table 2, were determined from Raison et al. (1991) and by simulating the build up of fine and

The predicted foliar N / P ratio of 28 for a 100-year-old stand was equal to that observed in old, uneven-aged E. sieberi forests in the OrbostCann River region of Victoria (Table 3). The modelled foliar nutrient concentrations were

Table 3 Foliage characteristics of a modelled E. sieberi stand in East Gippsland, Victoria, as compared to observed characteristics

Observed Modelled

Foliage prod. (kgm - 2 y r - t )

Foliar [N] (mgg 1)

Foliar [P] (mgg-1)

2.5 2.7

8.9 10.7

0.32 0.38

The values for the observed stand are average values for two uneven-aged stands growing on duplex and gradational soils, respectively, reported by Raison et al. (1993). Values for the even-aged modelled stand are for an age of 100 years.

D.A. King / Ecological Modelling 87 (1996) 181-203

194

somewhat greater than observed, due in part to repeated wildfires in the Orbost-Cann River region, which would cause greater nutrient losses and lower foliar nutrient concentrations than for the modelled case of no mid-rotation fires. The trajectories of overstorey and understorey leaf area index (LAI) for a 120-year rotation (Fig. 4a) indicate an interaction between these two layers, with understorey LAI increasing somewhat as the overstorey LAI declines in old stands. This interaction results in negligible change over time in the total fraction of light intercepted by both layers after stand closure. The pattern of accumulation of standing wood biomass over the rotation (Fig. 4a) is generally similar to the accumulation of standing wood biomass predicted by empirical models for Eucalyptus species (West and Mattay, 1993). The predicted net annual wood production declines with time (Fig. 5) due to the assumed age-related decline in production efficiency and the increase in wood lost to mortality with increasing stand

a) wood

3O

2O

E t~

oE

f]°0 i

b)

° a5

E

"6 ~ o8

i ine

-~ 04

~o2 ~

o

10

20

30

40

50

60

70

80

90

100

110

120

Stand age (yrs)

Fig. 5. Predicted annual overstorey wood production vs. stand age for an E. sieberi stand in East Gippsland, Victoria. Gross wood production includes all new wood in stems and larger branches (excluding bark) produced over the year. Net wood production is the net annual increase in standing wood dry mass in the stem and larger branches after subtraction of losses due to mortality.

biomass. The net wood production rate peaks at a somewhat earlier age than that indicated by the empirical yield model STANDSIM (John Coleman, CSIRO Division of Forestry, pers. commun.; Campbell et al., 1979). This difference is due in part to my assumption that mortality is a constant fraction of standing wood biomass throughout the rotation, rather than the more complex function of stand age and stem cross sectional area used in STANDSIM. Omission of the understorey from the model results in more rapid initial development of overstorey leaf area and greater wood production over the rotation (Fig. 4b) because more water and nutrients are then available to the overstorey.

I ~°

3.2. Influence of juvenile foliage on forest growth

0

o

~o

20

30

40

5O

60

70

e0

9O

100

110

~20

Stand age (yrs) Fig. 4. Predicted overstorey (heavy line) and understorey (light line) leaf area index and standing overstorey wood biomass plotted as a function of stand age, with and without an understorey (panels a and b, respectively), for E. sieberi in East Oippsland, Victoria.

Changing the length of time involved in shifting from the initial juvenile foliage to adult foliage had a strong impact on stand dynamics (Fig. 6), with a more prolonged juvenile period increasing the initial overstorey leaf area and growth rate and slowing the early growth of the understorey. Because juvenile leaves have greater specific leaf area than adult leaves, seedlings are able to intercept more light per unit foliage mass. The effect of this enhanced light interception is

D.A. King/ Ecological Modelling 87 (1996) 181-203

magnified in the early exponential phase of growth when a modest increase in the relative growth rate has a large effect on accumulated biomass. Omission of the juvenile stage greatly slowed the development of the overstorey (Fig. 6), due in part to compensatory growth and nutrient uptake by the understorey (Table 4). Thus, juvenile foliage is important in the regeneration of eucalypts after fire or other disturbances. Juvenile foliage is considered to be a primitive, ancestral character of the eucalypts (Pryor, 1976), which

195

Table 4 Impact of the length of the juvenile foliage phase on modelled wood production. Length of the juvenile phase is the time required to shift entirely to adult foliage Length of juvenile phase (yrs) 0 4 8 Case of no understorey 0 4 8

Standing above-ground wood 2) after

biomass (kg m 4 yrs

40 yrs

0.034 0.69 1.06

27.0 31.2 32.4

0.10 1.13 1.45

34.4 36.6 36.7

a)

b)

E

4

wood

c) is "i -

i[

2

j.oo0

a

1

2

3

a

5

6

r

a

9 10 11 12 ~3

14

15

18

l

~r ~s 1~ 2O

may have been retained for its role in promoting rapid early growth. These results are consistent with the high correlation between early wood production and the persistence of juvenile foliage reported by Beadle et al. (1989) in 2-to 4-year-old E. nitens plantations of different provenances, grown in the same locations. Juvenile foliage of E. nitens differs from that of E. sieberi in having a more horizontal orientation and persisting to a greater sapling age, further increasing the light interception of sapling E. nitens. However, predicted wood production over a 40-year rotation was much less affected by juvenile phase duration than was production over the first 4 years (Table 4), as mature canopy productivity was not affected by the juvenile phase (Fig. 6). Thus, caution is required in interpreting the results of short-term experiments, which are strongly affected by the initial exponential growth phase. Nonetheless, selection of species and populations with a pronounced juvenile phase may be advantageous for fibre production over short rotations, where rapid attainment of canopy closure has a greater impact on whole rotation production.

Stand age (yrs)

Fig. 6. Predicted overstorey (heavy line) and understorey (light line) leaf area index and standing overstorey wood biomass plotted as a function of stand age for the cases where the period of transition from juvenile to adult foliage is (a) 8, (b) 4 (base case), and (e) 0 years, i.e., no juvenile foliage is produced.

3.3. Long-term productivity The model implications for long-term production were assessed with 600-year simulations for the base case where all overstorey wood in the

D.A. King / Ecological Modelling 87 (1996) 181-203

196

80I 60

ses v

10

13h~N'vested 2o

g CD ,

i 10

~-- 0

i

i 20

i

a 30

i

i 40

i

i 50

k

L 60

i

i 70

d

i 8O

i

k 90

k

i tO0

i

i 110

i

i 120

Rotation length (yrs) Fig. 8. Projected amount of phosphorus lost in harvested wood, postharvest debris burns and leaching over 600 years, plotted as a function of harvest rotation length. The horizontal line indicates the cumulative 600-year input of phosphorus through atmospheric deposition.

b)

m

c) 4O

I

0 6OO

Time (yrs) Fig. 7. Predicted standing overstorey wood biomass over 600 years for E. sieberi in East Gippsland, Victoria, for harvest rotation lengths of (a) 120, (b) 60 and (c) 30 years. The horizontal line indicates the wood biomass attained at the end of the first rotation for each rotation length considered.

stems and large branches is removed at harvest, while all leaves, twigs and bark are left on site and burned along with the non-woody litter layer and understorey vegetation. As shown in Fig. 7, the predicted wood production of successive rotations increases for long rotations and decreases for short rotations, with production remaining unchanged for a rotation length of 79 years. Whether production declines or increases over multiple rotations depends entirely on the net balance of the limiting nutrient, phosphorus. Fig. 8 shows that the sum of P losses (primarily due to harvests and debris burns) is greatest for a short rotation length of 15 to 20 years and declines as rotation length is increased above this value. A

net loss of P is predicted for rotation lengths of less than 76 years when the losses exceed the cumulative atmospheric input. The predicted mean annual wood production (harvested wood/total growth time) for the first rotation attains a maximum at a stand age of 26 years (Fig. 9), similar to the age predicted by empirical yield tables for E. sieberi in East Gippsland (Borough et al., 1978). This age of peak mean annual production is substantially greater than the age of peak net annual production of Fig. 5 because the former quantity averages production from stand initiation (when production is nil) to the indicated age. However, the predicted

o.8

~j o8

¢~

:[

o2

o

10

2o

3o

40

50

60

70

80

90

100

110

120

Rotation length (yrs)

Fig. 9. Projected mean annual wood production (harvested stem and branchwood/total growth time) plotted as a function of rotation length for the first rotation (heavy line) and all rotations over a 600-year period (light line).

D.A. King/Ecological Modelling 87 (1996) 181-203

mean annual production over a period of 600 years, plotted as a function of rotation length, differs substantially from that determined for the first rotation. The net loss of P from the system for rotations shorter than 76 years causes production to decline over time, thereby reducing the long-term mean annual production below that predicted for the first rotation (Fig. 9). As a result, the maximum mean annual production over 600 years is lower than that of the first rotation and occurs at a longer rotation length of 34 years. The above patterns in long-term productivity would be shifted by different management scenarios. The removal of whole trees at harvest, including leaves, twigs and bark, as well as wood, increases the nutrient loss from the system, thereby increasing the rotation length required to Table 5 Predicted sustainable rotation length for specified managem e n t practices M a n a g e m e n t practice

Sustainable rotation length (yrs)

Base case No understorey All overstorey bark, twigs and leaves removed along with harvested wood No postharvest burning

79 103 114

42

In the base case, all overstorey tree bark, twigs and leaves are left on site and burned after harvest (along with above-ground nonwoody litter and understorey parts). Each of the other cases involves one change to the base case, as specified.

197

sustain production (Table 5). Omitting the understorey also increases the predicted sustainable rotation length because the resulting increase in overstorey wood production and nutrient concentration increases the nutrient loss in wood harvests. For 40-year rotations, omission of the understorey increases the first rotation wood harvest by 17%, while increasing the cumulative 600-year production by only 13%, due to this greater nutrient loss. In contrast, the cessation of postharvest burning substantially decreases the sustainable rotation length, as fire accounts for approximately 1/3 of the total P lost in the base case (Fig. 8). The latter assessment assumes that the understorey is cut but left on site) and the soil and litter are tilled mechanically, as is required for successful eucalypt regeneration if fire is not used to prepare the seed bed (Cremer et al., 1978). The sustainable rotation length would also be affected by changes in the amount of P input from the atmosphere or lost in wood harvest and fire. The estimate of P deposition is uncertain, as this quantity has not been extensively measured in Australia and may vary between sites depending on proximity to anthropogenic sources and wind patterns. The estimation of P losses is also subject to uncertainty, as the relative P concentration in wood vs. foliage may vary between eucalypt species by a factor of two (Attiwill and Leeper, 1987), while fire losses depend on fire intensity, controlled by air temperature and humidity. These uncertainties are addressed in Table 6, which shows the effects of + 50% changes in

Table 6 Influence of key factors on the sustainable rotation length, defined as the harvest rotation length for which the final rotation wood mass after 600 years equals the first rotation wood mass Factor

Sustainable rotation length (yrs) predicted with _+50% changes in the indicated factors

Atmospheric P deposition Wood P concentration relative to foliar P concentration Fraction of P lost from components burned after each harvest Base case

167 51 61

-

50%

+ 50%

45 122 108 79

All overstorey tree bark, twigs and leaves are left on site and burned after harvest (along with aboveground nonwoody litter and understorey parts) in each case modelled here.

198

D.A. King~Ecological Modelling 87 (1996) 181-203

atmospheric inputs, ratio of wood to foliage P concentration and fraction of P lost in debris burns. Atmospheric deposition had the largest impact on the predicted sustainable rotation length, which was inversely proportional to the P input (Table 6). The sustainable rotation length would also be affected by wildfires, which are difficult to exclude from highly flammable eucalypt forests, as judged from the history of wildfires in Australia (Pyne, 1991). Because the uncertainty in the predicted sustainable rotation length is of the same magnitude as the impact of different management practices, predictions concerning the latter should be viewed as relative and not absolute projections. For example, the conclusion that whole tree harvests increase the rotation length required for sustainable production agrees with other assessments of management impacts (e.g. Kimmins, 1977) and is more robust than the prediction of a particular sustainable rotation length. On the other hand, for the 26-year rotation maximizing the short-term mean annual production, long-term production is predicted to decline for all of the model variations and management practices considered in Tables 5 and 6. Thus, the maintenance of productivity in intensively managed, short-rotation plantations requires additional nutrient inputs, even with management to reduce nutrient losses.

3.4. Effects of fertilization on production The application of nutrients in fertilizers to replace those lost in harvested material and boost soil reserves and productivity is an increasingly common practice in the management of Pinus radiata plantations in Australia (Turner and Lambert, 1986). The response to fertilization was simulated by assuming that applied P initially enters the labile pool, as would be expected for highly soluble superphosphate fertilizers. Application of 5 g m -2 (50 kg ha -t) of P at the time of planting produced a manyfold increase in simulated wood accumulation over the first several years, similar to the fertilization response reported for seedlings in the Orbost-Cann River region (Raison et al., 1993) and in other eucalypt fertilization experiments (Cromer and Williams,

~?

14

~

o6

E

~o, "~ 02 Z o

1

2

3

4

5

6

7

8

Stand age (yrs)

9

iiiii

10

11

12

13

14

15

Fig. 10. Predicted net annual wood production for E. sieberi in East Gippsland Victoria, without fertilizer (light line) and with 5 g m -2 of P applied at the time of planting (heavy line), with adequate N to insure that P remains the growth-limiting nutrient.

1982). However, the relative impact of fertilization decreases with time (Fig. 10), as the initial difference in wood production rates is largely a consequence of enhanced leaf area and light interception early in the growth of the fertilized stand, similar to the early effect of juvenile foliage (Table 4, Fig. 6). The relative enhancement of P uptake is also greatest initially, because most P in the labile pool passes to the more tightly bound inorganic pool over a period of several years, as modelled here, where it is less available for plant uptake. The predicted 25% increase in wood production over a 40-year rotation associated with the above fertilization is substantial, although less than might be inferred directly from short-term experiments. Substantially greater enhancements in wood production in response to a similar-sized P application were reported for Pinus radiata grown for 30 years on a very P-deficient soil in Southeastern Australia (Turner and Lambert, 1986). However, P. radiata shows reduced growth at foliar P concentrations of 1 mg g-a (Turner and Lambert, 1986), three times the foliar P concentration observed in E sieberi in East Gippsland (Table 3). The predicted long-term response to 2 g P m -2 applied at the beginning of every 40-year rotation following the first harvest is shown in Fig. 11. Production rises in the first few rotations,

D.A. King/Ecological Modelling 87 (1996) 181-203

E 60

b)

E O ~5

4o

~

2o

6O

e)

2O I

o'

600

Time (yrs)

above 0.4 g m -2 are ineffective in promoting additional long-term growth if no N is added. The additional N input required to maintain a nutrient balance after P fertilization could arise in part from N fixation by legumes. Current rates of N fixation appear to be quite low in mature forests of the Orbost region, due to light and P limitation of understorey legumes (Raison et al., 1993). However, the native N fixer, Acacia myrtifolia, showed a very large increase in N accumulation in response to P fertilization when planted after logging and might contribute a substantial fraction of the additional N required on P-fertilized sites (Raison et al., 1993). The use of N fixers would have the added benefit of adding N in an organic form (litter) less subject to leaching than commercial N fertilizers (Beets and Madgwick, 1988). Thus, an understorey managed for N fixers might increase long-term production on P-fertilized sites, despite the 10 to 15% reduction in long-term wood production attributed to the presence of an understorey without N fixers. Given adequate N inputs, the benefits of P fertilization are projected to accumulate for centuries, for the case of 40-year rotations, shown in Fig. 12. During the first rotation, only 6% of the applied P is incorporated in wood, while over

Fig. 11. Predicted standing wood biomass over 600 years for 40-year rotations of E. sieberi in East Gippsland, Victoria for the case of (a) no fertilization, (b) 2 g m 2 p applied at the beginning of each rotation following the first, and (c) similar P additions as in (b), plus enough additional N to prevent this nutrient from limiting growth after P fertilization.

losses Firelosses

i f Leaching

f

lOO

i but then declines due to limitation of growth by nitrogen in later rotations when the projected foliar N / P ratio declines below the assumed critical value of 20. However, if the N input of 0.4 g m -2 yr - t due to atmospheric deposition is increased to 1.4 g m - 2 y r - t by additional inputs, P remains the growth-limiting nutrient, and production continues to increase over the 600-year period as P builds up in both organic and inorganic soil pools. The model predicts an almost linear increase in long-term production as the applied P is increased from 0 to 2 g m -2 rotation -1, given adequate N. On the other hand, P fertilizations

199

~

"

"

Harvested wood

~

Soil and litter

40

~ 2o o

0

1

2

3

4

5

'

6

7

8

9

to

11

12

13

t4

Rotationsafterbeginningfertilization Fig. 12. Relative accumulation of P added in fertilizer in different components, for E. sieberi grown on a 40-year rotation, with 1 g m -2 of P applied per rotation and adequate N inputs to insure that N does not limit growth. The applied P accumulation in a given component was calculated as the difference between the amounts of P in the component with and without fertilization.

200

D.A. King / Ecological Modelling 87 (1996) 181-203

Table 7 Phosphorus pool sizes and turnover times projected for a 40-year-old unfertilized stand of E. sieberi Phosphorus pool Pool size Pool turnover (g P m -2) time (yrs) Live vegetation Fine litter Woody litter Slow soil organic matter Passive soil organic matter Inorganic P Labile P

1.7 1.0 0.3 4.5 5.0 5.5 0.2

6.8 4,3 25 25 650 120 2.4

Inorganic P refers to phosphorus which is bound to the soil in iron and aluminum complexes that can potentially enter the organic P cycle, but does not include occluded P which remains completely unavailable to trees.

90% of this P remains in the soil and litter pools. However, over 600 years, the fraction of total applied P accumulated in harvested wood increases to 26%. This long-term cumulative response to P fertilization can be related to the sizes and turnover rates of the different P pools, shown in Table 7. Most of the P added to the labile pool enters the inorganic P pool over the first few years, i.e., it is bound to the soil. P entering the vegetation is rapidly cycled into the soil organic matter pools through litter production, while P in the inorganic pool is slowly solublized by roots and shifted into the organic pools, as modelled here. Because the inorganic and passive organic P pools are large and have turnover times of one and six centuries, respectively (Table 7), the applied P is predicted to have long-term effects in addition to the initial impact on growth shown in Fig. 10. Experimental evidence for such long-term benefits is difficult to acquire, although the observation of elevated wood production and foliar and soil P concentrations in a Pinus radiata stand, two rotations after fertilization (Gentle et al., 1986), is consistent with these predictions. 3.5. Caveats

As with any model of living systems, numerous approximations and idealizations have been made

in projecting forest growth. Major approximations include: 1. The assumption of laterally uniform distributions of leaves, roots and nutrients, with no regard for canopy gaps and below-ground heterogeneity which occur in real forests. 2. No inclusion of occasional events which could disrupt forest development, such as pest and pathogen outbreaks, extreme droughts and severe fires. 3. No inclusion of possible impacts of logging on factors other than P and N cycling, such as loss of other nutrients and soil erosion and compaction by heavy machines (Sands et al,, 1979; Lacey, 1993), which may reduce future production on old skid trails (Firth and Murphy, 1989). 4. Many of the parameters are uncertain, particularly regarding the phosphorus cycle, where it is difficult to measure the transfer rates among those pools which are not spatially separated. Note also, that the formulation was chosen for E. sieberi on sandy, P-deficient soils, and may not apply to other eucalypts on other sites. Making these assumptions has made the development, parameterization and presentation of the model much more feasible than would otherwise be the case. However, the resulting projections apply only for the ideal case of a uniform, healthy stand, and may be biased by uncertainties in the assumed mechanisms of forest growth. Thus, the results should be viewed as showing how different factors may interact to influence forest growth, rather than as realistic projections of future production.

Acknowledgements I thank R. McMurtrie and P. Khanna for helpful reviews of the manuscript and J. Raison, M. Kirschbaum, H. Keith and M. Connell for discussions of the approach and data from their East Gippsland research site. This work was supported by the N G A C Dedicated Greenhouse Research Grants Scheme and the Australian Research Council.

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